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How Are Vectors Multiplied?
How Are Vectors Multiplied?
Chloe Bennett••6 min read
In mathematics, Vector multiplication
Vector multiplication
The cross product a × b is defined as a vector c that is perpendicular (orthogonal) to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span.
refers to one of several techniques for the multiplication of two (or more) vectors with themselves. ... Alternatively, it is defined as the product of the projection of the first vector onto the second vector and the magnitude of the second vector. Thus, A ⋅ B = |A| |B| cos θ
Why do we multiply vectors?
Multiplication of a vector by a scalar changes the magnitude of the vector, but leaves its direction unchanged. The scalar changes the size of the vector. The scalar "scales" the vector.
What happens when a vector is multiplied by?
When a vector is multiplied by a scalar, the size of the vector is “scaled” up or down. Multiplying a vector by a positive scalar will only change its magnitude, not its direction. When a vector is multiplied by a negative scalar, the direction will be reversed.
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